core/num/
f64.rs

1//! Constants for the `f64` double-precision floating point type.
2//!
3//! *[See also the `f64` primitive type][f64].*
4//!
5//! Mathematically significant numbers are provided in the `consts` sub-module.
6//!
7//! For the constants defined directly in this module
8//! (as distinct from those defined in the `consts` sub-module),
9//! new code should instead use the associated constants
10//! defined directly on the `f64` type.
11
12#![stable(feature = "rust1", since = "1.0.0")]
13
14use crate::convert::FloatToInt;
15use crate::num::FpCategory;
16use crate::panic::const_assert;
17use crate::{intrinsics, mem};
18
19/// The radix or base of the internal representation of `f64`.
20/// Use [`f64::RADIX`] instead.
21///
22/// # Examples
23///
24/// ```rust
25/// // deprecated way
26/// # #[allow(deprecated, deprecated_in_future)]
27/// let r = std::f64::RADIX;
28///
29/// // intended way
30/// let r = f64::RADIX;
31/// ```
32#[stable(feature = "rust1", since = "1.0.0")]
33#[deprecated(since = "TBD", note = "replaced by the `RADIX` associated constant on `f64`")]
34#[rustc_diagnostic_item = "f64_legacy_const_radix"]
35pub const RADIX: u32 = f64::RADIX;
36
37/// Number of significant digits in base 2.
38/// Use [`f64::MANTISSA_DIGITS`] instead.
39///
40/// # Examples
41///
42/// ```rust
43/// // deprecated way
44/// # #[allow(deprecated, deprecated_in_future)]
45/// let d = std::f64::MANTISSA_DIGITS;
46///
47/// // intended way
48/// let d = f64::MANTISSA_DIGITS;
49/// ```
50#[stable(feature = "rust1", since = "1.0.0")]
51#[deprecated(
52    since = "TBD",
53    note = "replaced by the `MANTISSA_DIGITS` associated constant on `f64`"
54)]
55#[rustc_diagnostic_item = "f64_legacy_const_mantissa_dig"]
56pub const MANTISSA_DIGITS: u32 = f64::MANTISSA_DIGITS;
57
58/// Approximate number of significant digits in base 10.
59/// Use [`f64::DIGITS`] instead.
60///
61/// # Examples
62///
63/// ```rust
64/// // deprecated way
65/// # #[allow(deprecated, deprecated_in_future)]
66/// let d = std::f64::DIGITS;
67///
68/// // intended way
69/// let d = f64::DIGITS;
70/// ```
71#[stable(feature = "rust1", since = "1.0.0")]
72#[deprecated(since = "TBD", note = "replaced by the `DIGITS` associated constant on `f64`")]
73#[rustc_diagnostic_item = "f64_legacy_const_digits"]
74pub const DIGITS: u32 = f64::DIGITS;
75
76/// [Machine epsilon] value for `f64`.
77/// Use [`f64::EPSILON`] instead.
78///
79/// This is the difference between `1.0` and the next larger representable number.
80///
81/// [Machine epsilon]: https://en.wikipedia.org/wiki/Machine_epsilon
82///
83/// # Examples
84///
85/// ```rust
86/// // deprecated way
87/// # #[allow(deprecated, deprecated_in_future)]
88/// let e = std::f64::EPSILON;
89///
90/// // intended way
91/// let e = f64::EPSILON;
92/// ```
93#[stable(feature = "rust1", since = "1.0.0")]
94#[deprecated(since = "TBD", note = "replaced by the `EPSILON` associated constant on `f64`")]
95#[rustc_diagnostic_item = "f64_legacy_const_epsilon"]
96pub const EPSILON: f64 = f64::EPSILON;
97
98/// Smallest finite `f64` value.
99/// Use [`f64::MIN`] instead.
100///
101/// # Examples
102///
103/// ```rust
104/// // deprecated way
105/// # #[allow(deprecated, deprecated_in_future)]
106/// let min = std::f64::MIN;
107///
108/// // intended way
109/// let min = f64::MIN;
110/// ```
111#[stable(feature = "rust1", since = "1.0.0")]
112#[deprecated(since = "TBD", note = "replaced by the `MIN` associated constant on `f64`")]
113#[rustc_diagnostic_item = "f64_legacy_const_min"]
114pub const MIN: f64 = f64::MIN;
115
116/// Smallest positive normal `f64` value.
117/// Use [`f64::MIN_POSITIVE`] instead.
118///
119/// # Examples
120///
121/// ```rust
122/// // deprecated way
123/// # #[allow(deprecated, deprecated_in_future)]
124/// let min = std::f64::MIN_POSITIVE;
125///
126/// // intended way
127/// let min = f64::MIN_POSITIVE;
128/// ```
129#[stable(feature = "rust1", since = "1.0.0")]
130#[deprecated(since = "TBD", note = "replaced by the `MIN_POSITIVE` associated constant on `f64`")]
131#[rustc_diagnostic_item = "f64_legacy_const_min_positive"]
132pub const MIN_POSITIVE: f64 = f64::MIN_POSITIVE;
133
134/// Largest finite `f64` value.
135/// Use [`f64::MAX`] instead.
136///
137/// # Examples
138///
139/// ```rust
140/// // deprecated way
141/// # #[allow(deprecated, deprecated_in_future)]
142/// let max = std::f64::MAX;
143///
144/// // intended way
145/// let max = f64::MAX;
146/// ```
147#[stable(feature = "rust1", since = "1.0.0")]
148#[deprecated(since = "TBD", note = "replaced by the `MAX` associated constant on `f64`")]
149#[rustc_diagnostic_item = "f64_legacy_const_max"]
150pub const MAX: f64 = f64::MAX;
151
152/// One greater than the minimum possible normal power of 2 exponent.
153/// Use [`f64::MIN_EXP`] instead.
154///
155/// # Examples
156///
157/// ```rust
158/// // deprecated way
159/// # #[allow(deprecated, deprecated_in_future)]
160/// let min = std::f64::MIN_EXP;
161///
162/// // intended way
163/// let min = f64::MIN_EXP;
164/// ```
165#[stable(feature = "rust1", since = "1.0.0")]
166#[deprecated(since = "TBD", note = "replaced by the `MIN_EXP` associated constant on `f64`")]
167#[rustc_diagnostic_item = "f64_legacy_const_min_exp"]
168pub const MIN_EXP: i32 = f64::MIN_EXP;
169
170/// Maximum possible power of 2 exponent.
171/// Use [`f64::MAX_EXP`] instead.
172///
173/// # Examples
174///
175/// ```rust
176/// // deprecated way
177/// # #[allow(deprecated, deprecated_in_future)]
178/// let max = std::f64::MAX_EXP;
179///
180/// // intended way
181/// let max = f64::MAX_EXP;
182/// ```
183#[stable(feature = "rust1", since = "1.0.0")]
184#[deprecated(since = "TBD", note = "replaced by the `MAX_EXP` associated constant on `f64`")]
185#[rustc_diagnostic_item = "f64_legacy_const_max_exp"]
186pub const MAX_EXP: i32 = f64::MAX_EXP;
187
188/// Minimum possible normal power of 10 exponent.
189/// Use [`f64::MIN_10_EXP`] instead.
190///
191/// # Examples
192///
193/// ```rust
194/// // deprecated way
195/// # #[allow(deprecated, deprecated_in_future)]
196/// let min = std::f64::MIN_10_EXP;
197///
198/// // intended way
199/// let min = f64::MIN_10_EXP;
200/// ```
201#[stable(feature = "rust1", since = "1.0.0")]
202#[deprecated(since = "TBD", note = "replaced by the `MIN_10_EXP` associated constant on `f64`")]
203#[rustc_diagnostic_item = "f64_legacy_const_min_10_exp"]
204pub const MIN_10_EXP: i32 = f64::MIN_10_EXP;
205
206/// Maximum possible power of 10 exponent.
207/// Use [`f64::MAX_10_EXP`] instead.
208///
209/// # Examples
210///
211/// ```rust
212/// // deprecated way
213/// # #[allow(deprecated, deprecated_in_future)]
214/// let max = std::f64::MAX_10_EXP;
215///
216/// // intended way
217/// let max = f64::MAX_10_EXP;
218/// ```
219#[stable(feature = "rust1", since = "1.0.0")]
220#[deprecated(since = "TBD", note = "replaced by the `MAX_10_EXP` associated constant on `f64`")]
221#[rustc_diagnostic_item = "f64_legacy_const_max_10_exp"]
222pub const MAX_10_EXP: i32 = f64::MAX_10_EXP;
223
224/// Not a Number (NaN).
225/// Use [`f64::NAN`] instead.
226///
227/// # Examples
228///
229/// ```rust
230/// // deprecated way
231/// # #[allow(deprecated, deprecated_in_future)]
232/// let nan = std::f64::NAN;
233///
234/// // intended way
235/// let nan = f64::NAN;
236/// ```
237#[stable(feature = "rust1", since = "1.0.0")]
238#[deprecated(since = "TBD", note = "replaced by the `NAN` associated constant on `f64`")]
239#[rustc_diagnostic_item = "f64_legacy_const_nan"]
240pub const NAN: f64 = f64::NAN;
241
242/// Infinity (∞).
243/// Use [`f64::INFINITY`] instead.
244///
245/// # Examples
246///
247/// ```rust
248/// // deprecated way
249/// # #[allow(deprecated, deprecated_in_future)]
250/// let inf = std::f64::INFINITY;
251///
252/// // intended way
253/// let inf = f64::INFINITY;
254/// ```
255#[stable(feature = "rust1", since = "1.0.0")]
256#[deprecated(since = "TBD", note = "replaced by the `INFINITY` associated constant on `f64`")]
257#[rustc_diagnostic_item = "f64_legacy_const_infinity"]
258pub const INFINITY: f64 = f64::INFINITY;
259
260/// Negative infinity (−∞).
261/// Use [`f64::NEG_INFINITY`] instead.
262///
263/// # Examples
264///
265/// ```rust
266/// // deprecated way
267/// # #[allow(deprecated, deprecated_in_future)]
268/// let ninf = std::f64::NEG_INFINITY;
269///
270/// // intended way
271/// let ninf = f64::NEG_INFINITY;
272/// ```
273#[stable(feature = "rust1", since = "1.0.0")]
274#[deprecated(since = "TBD", note = "replaced by the `NEG_INFINITY` associated constant on `f64`")]
275#[rustc_diagnostic_item = "f64_legacy_const_neg_infinity"]
276pub const NEG_INFINITY: f64 = f64::NEG_INFINITY;
277
278/// Basic mathematical constants.
279#[stable(feature = "rust1", since = "1.0.0")]
280pub mod consts {
281    // FIXME: replace with mathematical constants from cmath.
282
283    /// Archimedes' constant (π)
284    #[stable(feature = "rust1", since = "1.0.0")]
285    pub const PI: f64 = 3.14159265358979323846264338327950288_f64;
286
287    /// The full circle constant (τ)
288    ///
289    /// Equal to 2π.
290    #[stable(feature = "tau_constant", since = "1.47.0")]
291    pub const TAU: f64 = 6.28318530717958647692528676655900577_f64;
292
293    /// The golden ratio (φ)
294    #[unstable(feature = "more_float_constants", issue = "103883")]
295    pub const PHI: f64 = 1.618033988749894848204586834365638118_f64;
296
297    /// The Euler-Mascheroni constant (γ)
298    #[unstable(feature = "more_float_constants", issue = "103883")]
299    pub const EGAMMA: f64 = 0.577215664901532860606512090082402431_f64;
300
301    /// π/2
302    #[stable(feature = "rust1", since = "1.0.0")]
303    pub const FRAC_PI_2: f64 = 1.57079632679489661923132169163975144_f64;
304
305    /// π/3
306    #[stable(feature = "rust1", since = "1.0.0")]
307    pub const FRAC_PI_3: f64 = 1.04719755119659774615421446109316763_f64;
308
309    /// π/4
310    #[stable(feature = "rust1", since = "1.0.0")]
311    pub const FRAC_PI_4: f64 = 0.785398163397448309615660845819875721_f64;
312
313    /// π/6
314    #[stable(feature = "rust1", since = "1.0.0")]
315    pub const FRAC_PI_6: f64 = 0.52359877559829887307710723054658381_f64;
316
317    /// π/8
318    #[stable(feature = "rust1", since = "1.0.0")]
319    pub const FRAC_PI_8: f64 = 0.39269908169872415480783042290993786_f64;
320
321    /// 1/π
322    #[stable(feature = "rust1", since = "1.0.0")]
323    pub const FRAC_1_PI: f64 = 0.318309886183790671537767526745028724_f64;
324
325    /// 1/sqrt(π)
326    #[unstable(feature = "more_float_constants", issue = "103883")]
327    pub const FRAC_1_SQRT_PI: f64 = 0.564189583547756286948079451560772586_f64;
328
329    /// 1/sqrt(2π)
330    #[doc(alias = "FRAC_1_SQRT_TAU")]
331    #[unstable(feature = "more_float_constants", issue = "103883")]
332    pub const FRAC_1_SQRT_2PI: f64 = 0.398942280401432677939946059934381868_f64;
333
334    /// 2/π
335    #[stable(feature = "rust1", since = "1.0.0")]
336    pub const FRAC_2_PI: f64 = 0.636619772367581343075535053490057448_f64;
337
338    /// 2/sqrt(π)
339    #[stable(feature = "rust1", since = "1.0.0")]
340    pub const FRAC_2_SQRT_PI: f64 = 1.12837916709551257389615890312154517_f64;
341
342    /// sqrt(2)
343    #[stable(feature = "rust1", since = "1.0.0")]
344    pub const SQRT_2: f64 = 1.41421356237309504880168872420969808_f64;
345
346    /// 1/sqrt(2)
347    #[stable(feature = "rust1", since = "1.0.0")]
348    pub const FRAC_1_SQRT_2: f64 = 0.707106781186547524400844362104849039_f64;
349
350    /// sqrt(3)
351    #[unstable(feature = "more_float_constants", issue = "103883")]
352    pub const SQRT_3: f64 = 1.732050807568877293527446341505872367_f64;
353
354    /// 1/sqrt(3)
355    #[unstable(feature = "more_float_constants", issue = "103883")]
356    pub const FRAC_1_SQRT_3: f64 = 0.577350269189625764509148780501957456_f64;
357
358    /// Euler's number (e)
359    #[stable(feature = "rust1", since = "1.0.0")]
360    pub const E: f64 = 2.71828182845904523536028747135266250_f64;
361
362    /// log<sub>2</sub>(10)
363    #[stable(feature = "extra_log_consts", since = "1.43.0")]
364    pub const LOG2_10: f64 = 3.32192809488736234787031942948939018_f64;
365
366    /// log<sub>2</sub>(e)
367    #[stable(feature = "rust1", since = "1.0.0")]
368    pub const LOG2_E: f64 = 1.44269504088896340735992468100189214_f64;
369
370    /// log<sub>10</sub>(2)
371    #[stable(feature = "extra_log_consts", since = "1.43.0")]
372    pub const LOG10_2: f64 = 0.301029995663981195213738894724493027_f64;
373
374    /// log<sub>10</sub>(e)
375    #[stable(feature = "rust1", since = "1.0.0")]
376    pub const LOG10_E: f64 = 0.434294481903251827651128918916605082_f64;
377
378    /// ln(2)
379    #[stable(feature = "rust1", since = "1.0.0")]
380    pub const LN_2: f64 = 0.693147180559945309417232121458176568_f64;
381
382    /// ln(10)
383    #[stable(feature = "rust1", since = "1.0.0")]
384    pub const LN_10: f64 = 2.30258509299404568401799145468436421_f64;
385}
386
387impl f64 {
388    /// The radix or base of the internal representation of `f64`.
389    #[stable(feature = "assoc_int_consts", since = "1.43.0")]
390    pub const RADIX: u32 = 2;
391
392    /// Number of significant digits in base 2.
393    ///
394    /// Note that the size of the mantissa in the bitwise representation is one
395    /// smaller than this since the leading 1 is not stored explicitly.
396    #[stable(feature = "assoc_int_consts", since = "1.43.0")]
397    pub const MANTISSA_DIGITS: u32 = 53;
398    /// Approximate number of significant digits in base 10.
399    ///
400    /// This is the maximum <i>x</i> such that any decimal number with <i>x</i>
401    /// significant digits can be converted to `f64` and back without loss.
402    ///
403    /// Equal to floor(log<sub>10</sub>&nbsp;2<sup>[`MANTISSA_DIGITS`]&nbsp;&minus;&nbsp;1</sup>).
404    ///
405    /// [`MANTISSA_DIGITS`]: f64::MANTISSA_DIGITS
406    #[stable(feature = "assoc_int_consts", since = "1.43.0")]
407    pub const DIGITS: u32 = 15;
408
409    /// [Machine epsilon] value for `f64`.
410    ///
411    /// This is the difference between `1.0` and the next larger representable number.
412    ///
413    /// Equal to 2<sup>1&nbsp;&minus;&nbsp;[`MANTISSA_DIGITS`]</sup>.
414    ///
415    /// [Machine epsilon]: https://en.wikipedia.org/wiki/Machine_epsilon
416    /// [`MANTISSA_DIGITS`]: f64::MANTISSA_DIGITS
417    #[stable(feature = "assoc_int_consts", since = "1.43.0")]
418    #[rustc_diagnostic_item = "f64_epsilon"]
419    pub const EPSILON: f64 = 2.2204460492503131e-16_f64;
420
421    /// Smallest finite `f64` value.
422    ///
423    /// Equal to &minus;[`MAX`].
424    ///
425    /// [`MAX`]: f64::MAX
426    #[stable(feature = "assoc_int_consts", since = "1.43.0")]
427    pub const MIN: f64 = -1.7976931348623157e+308_f64;
428    /// Smallest positive normal `f64` value.
429    ///
430    /// Equal to 2<sup>[`MIN_EXP`]&nbsp;&minus;&nbsp;1</sup>.
431    ///
432    /// [`MIN_EXP`]: f64::MIN_EXP
433    #[stable(feature = "assoc_int_consts", since = "1.43.0")]
434    pub const MIN_POSITIVE: f64 = 2.2250738585072014e-308_f64;
435    /// Largest finite `f64` value.
436    ///
437    /// Equal to
438    /// (1&nbsp;&minus;&nbsp;2<sup>&minus;[`MANTISSA_DIGITS`]</sup>)&nbsp;2<sup>[`MAX_EXP`]</sup>.
439    ///
440    /// [`MANTISSA_DIGITS`]: f64::MANTISSA_DIGITS
441    /// [`MAX_EXP`]: f64::MAX_EXP
442    #[stable(feature = "assoc_int_consts", since = "1.43.0")]
443    pub const MAX: f64 = 1.7976931348623157e+308_f64;
444
445    /// One greater than the minimum possible *normal* power of 2 exponent
446    /// for a significand bounded by 1 ≤ x < 2 (i.e. the IEEE definition).
447    ///
448    /// This corresponds to the exact minimum possible *normal* power of 2 exponent
449    /// for a significand bounded by 0.5 ≤ x < 1 (i.e. the C definition).
450    /// In other words, all normal numbers representable by this type are
451    /// greater than or equal to 0.5&nbsp;×&nbsp;2<sup><i>MIN_EXP</i></sup>.
452    #[stable(feature = "assoc_int_consts", since = "1.43.0")]
453    pub const MIN_EXP: i32 = -1021;
454    /// One greater than the maximum possible power of 2 exponent
455    /// for a significand bounded by 1 ≤ x < 2 (i.e. the IEEE definition).
456    ///
457    /// This corresponds to the exact maximum possible power of 2 exponent
458    /// for a significand bounded by 0.5 ≤ x < 1 (i.e. the C definition).
459    /// In other words, all numbers representable by this type are
460    /// strictly less than 2<sup><i>MAX_EXP</i></sup>.
461    #[stable(feature = "assoc_int_consts", since = "1.43.0")]
462    pub const MAX_EXP: i32 = 1024;
463
464    /// Minimum <i>x</i> for which 10<sup><i>x</i></sup> is normal.
465    ///
466    /// Equal to ceil(log<sub>10</sub>&nbsp;[`MIN_POSITIVE`]).
467    ///
468    /// [`MIN_POSITIVE`]: f64::MIN_POSITIVE
469    #[stable(feature = "assoc_int_consts", since = "1.43.0")]
470    pub const MIN_10_EXP: i32 = -307;
471    /// Maximum <i>x</i> for which 10<sup><i>x</i></sup> is normal.
472    ///
473    /// Equal to floor(log<sub>10</sub>&nbsp;[`MAX`]).
474    ///
475    /// [`MAX`]: f64::MAX
476    #[stable(feature = "assoc_int_consts", since = "1.43.0")]
477    pub const MAX_10_EXP: i32 = 308;
478
479    /// Not a Number (NaN).
480    ///
481    /// Note that IEEE 754 doesn't define just a single NaN value; a plethora of bit patterns are
482    /// considered to be NaN. Furthermore, the standard makes a difference between a "signaling" and
483    /// a "quiet" NaN, and allows inspecting its "payload" (the unspecified bits in the bit pattern)
484    /// and its sign. See the [specification of NaN bit patterns](f32#nan-bit-patterns) for more
485    /// info.
486    ///
487    /// This constant is guaranteed to be a quiet NaN (on targets that follow the Rust assumptions
488    /// that the quiet/signaling bit being set to 1 indicates a quiet NaN). Beyond that, nothing is
489    /// guaranteed about the specific bit pattern chosen here: both payload and sign are arbitrary.
490    /// The concrete bit pattern may change across Rust versions and target platforms.
491    #[rustc_diagnostic_item = "f64_nan"]
492    #[stable(feature = "assoc_int_consts", since = "1.43.0")]
493    #[allow(clippy::eq_op)]
494    pub const NAN: f64 = 0.0_f64 / 0.0_f64;
495    /// Infinity (∞).
496    #[stable(feature = "assoc_int_consts", since = "1.43.0")]
497    pub const INFINITY: f64 = 1.0_f64 / 0.0_f64;
498    /// Negative infinity (−∞).
499    #[stable(feature = "assoc_int_consts", since = "1.43.0")]
500    pub const NEG_INFINITY: f64 = -1.0_f64 / 0.0_f64;
501
502    /// Sign bit
503    pub(crate) const SIGN_MASK: u64 = 0x8000_0000_0000_0000;
504
505    /// Exponent mask
506    pub(crate) const EXP_MASK: u64 = 0x7ff0_0000_0000_0000;
507
508    /// Mantissa mask
509    pub(crate) const MAN_MASK: u64 = 0x000f_ffff_ffff_ffff;
510
511    /// Minimum representable positive value (min subnormal)
512    const TINY_BITS: u64 = 0x1;
513
514    /// Minimum representable negative value (min negative subnormal)
515    const NEG_TINY_BITS: u64 = Self::TINY_BITS | Self::SIGN_MASK;
516
517    /// Returns `true` if this value is NaN.
518    ///
519    /// ```
520    /// let nan = f64::NAN;
521    /// let f = 7.0_f64;
522    ///
523    /// assert!(nan.is_nan());
524    /// assert!(!f.is_nan());
525    /// ```
526    #[must_use]
527    #[stable(feature = "rust1", since = "1.0.0")]
528    #[rustc_const_stable(feature = "const_float_classify", since = "1.83.0")]
529    #[inline]
530    #[allow(clippy::eq_op)] // > if you intended to check if the operand is NaN, use `.is_nan()` instead :)
531    pub const fn is_nan(self) -> bool {
532        self != self
533    }
534
535    /// Returns `true` if this value is positive infinity or negative infinity, and
536    /// `false` otherwise.
537    ///
538    /// ```
539    /// let f = 7.0f64;
540    /// let inf = f64::INFINITY;
541    /// let neg_inf = f64::NEG_INFINITY;
542    /// let nan = f64::NAN;
543    ///
544    /// assert!(!f.is_infinite());
545    /// assert!(!nan.is_infinite());
546    ///
547    /// assert!(inf.is_infinite());
548    /// assert!(neg_inf.is_infinite());
549    /// ```
550    #[must_use]
551    #[stable(feature = "rust1", since = "1.0.0")]
552    #[rustc_const_stable(feature = "const_float_classify", since = "1.83.0")]
553    #[inline]
554    pub const fn is_infinite(self) -> bool {
555        // Getting clever with transmutation can result in incorrect answers on some FPUs
556        // FIXME: alter the Rust <-> Rust calling convention to prevent this problem.
557        // See https://github.com/rust-lang/rust/issues/72327
558        (self == f64::INFINITY) | (self == f64::NEG_INFINITY)
559    }
560
561    /// Returns `true` if this number is neither infinite nor NaN.
562    ///
563    /// ```
564    /// let f = 7.0f64;
565    /// let inf: f64 = f64::INFINITY;
566    /// let neg_inf: f64 = f64::NEG_INFINITY;
567    /// let nan: f64 = f64::NAN;
568    ///
569    /// assert!(f.is_finite());
570    ///
571    /// assert!(!nan.is_finite());
572    /// assert!(!inf.is_finite());
573    /// assert!(!neg_inf.is_finite());
574    /// ```
575    #[must_use]
576    #[stable(feature = "rust1", since = "1.0.0")]
577    #[rustc_const_stable(feature = "const_float_classify", since = "1.83.0")]
578    #[inline]
579    pub const fn is_finite(self) -> bool {
580        // There's no need to handle NaN separately: if self is NaN,
581        // the comparison is not true, exactly as desired.
582        self.abs() < Self::INFINITY
583    }
584
585    /// Returns `true` if the number is [subnormal].
586    ///
587    /// ```
588    /// let min = f64::MIN_POSITIVE; // 2.2250738585072014e-308_f64
589    /// let max = f64::MAX;
590    /// let lower_than_min = 1.0e-308_f64;
591    /// let zero = 0.0_f64;
592    ///
593    /// assert!(!min.is_subnormal());
594    /// assert!(!max.is_subnormal());
595    ///
596    /// assert!(!zero.is_subnormal());
597    /// assert!(!f64::NAN.is_subnormal());
598    /// assert!(!f64::INFINITY.is_subnormal());
599    /// // Values between `0` and `min` are Subnormal.
600    /// assert!(lower_than_min.is_subnormal());
601    /// ```
602    /// [subnormal]: https://en.wikipedia.org/wiki/Denormal_number
603    #[must_use]
604    #[stable(feature = "is_subnormal", since = "1.53.0")]
605    #[rustc_const_stable(feature = "const_float_classify", since = "1.83.0")]
606    #[inline]
607    pub const fn is_subnormal(self) -> bool {
608        matches!(self.classify(), FpCategory::Subnormal)
609    }
610
611    /// Returns `true` if the number is neither zero, infinite,
612    /// [subnormal], or NaN.
613    ///
614    /// ```
615    /// let min = f64::MIN_POSITIVE; // 2.2250738585072014e-308f64
616    /// let max = f64::MAX;
617    /// let lower_than_min = 1.0e-308_f64;
618    /// let zero = 0.0f64;
619    ///
620    /// assert!(min.is_normal());
621    /// assert!(max.is_normal());
622    ///
623    /// assert!(!zero.is_normal());
624    /// assert!(!f64::NAN.is_normal());
625    /// assert!(!f64::INFINITY.is_normal());
626    /// // Values between `0` and `min` are Subnormal.
627    /// assert!(!lower_than_min.is_normal());
628    /// ```
629    /// [subnormal]: https://en.wikipedia.org/wiki/Denormal_number
630    #[must_use]
631    #[stable(feature = "rust1", since = "1.0.0")]
632    #[rustc_const_stable(feature = "const_float_classify", since = "1.83.0")]
633    #[inline]
634    pub const fn is_normal(self) -> bool {
635        matches!(self.classify(), FpCategory::Normal)
636    }
637
638    /// Returns the floating point category of the number. If only one property
639    /// is going to be tested, it is generally faster to use the specific
640    /// predicate instead.
641    ///
642    /// ```
643    /// use std::num::FpCategory;
644    ///
645    /// let num = 12.4_f64;
646    /// let inf = f64::INFINITY;
647    ///
648    /// assert_eq!(num.classify(), FpCategory::Normal);
649    /// assert_eq!(inf.classify(), FpCategory::Infinite);
650    /// ```
651    #[stable(feature = "rust1", since = "1.0.0")]
652    #[rustc_const_stable(feature = "const_float_classify", since = "1.83.0")]
653    pub const fn classify(self) -> FpCategory {
654        // We used to have complicated logic here that avoids the simple bit-based tests to work
655        // around buggy codegen for x87 targets (see
656        // https://github.com/rust-lang/rust/issues/114479). However, some LLVM versions later, none
657        // of our tests is able to find any difference between the complicated and the naive
658        // version, so now we are back to the naive version.
659        let b = self.to_bits();
660        match (b & Self::MAN_MASK, b & Self::EXP_MASK) {
661            (0, Self::EXP_MASK) => FpCategory::Infinite,
662            (_, Self::EXP_MASK) => FpCategory::Nan,
663            (0, 0) => FpCategory::Zero,
664            (_, 0) => FpCategory::Subnormal,
665            _ => FpCategory::Normal,
666        }
667    }
668
669    /// Returns `true` if `self` has a positive sign, including `+0.0`, NaNs with
670    /// positive sign bit and positive infinity.
671    ///
672    /// Note that IEEE 754 doesn't assign any meaning to the sign bit in case of
673    /// a NaN, and as Rust doesn't guarantee that the bit pattern of NaNs are
674    /// conserved over arithmetic operations, the result of `is_sign_positive` on
675    /// a NaN might produce an unexpected or non-portable result. See the [specification
676    /// of NaN bit patterns](f32#nan-bit-patterns) for more info. Use `self.signum() == 1.0`
677    /// if you need fully portable behavior (will return `false` for all NaNs).
678    ///
679    /// ```
680    /// let f = 7.0_f64;
681    /// let g = -7.0_f64;
682    ///
683    /// assert!(f.is_sign_positive());
684    /// assert!(!g.is_sign_positive());
685    /// ```
686    #[must_use]
687    #[stable(feature = "rust1", since = "1.0.0")]
688    #[rustc_const_stable(feature = "const_float_classify", since = "1.83.0")]
689    #[inline]
690    pub const fn is_sign_positive(self) -> bool {
691        !self.is_sign_negative()
692    }
693
694    #[must_use]
695    #[stable(feature = "rust1", since = "1.0.0")]
696    #[deprecated(since = "1.0.0", note = "renamed to is_sign_positive")]
697    #[inline]
698    #[doc(hidden)]
699    pub fn is_positive(self) -> bool {
700        self.is_sign_positive()
701    }
702
703    /// Returns `true` if `self` has a negative sign, including `-0.0`, NaNs with
704    /// negative sign bit and negative infinity.
705    ///
706    /// Note that IEEE 754 doesn't assign any meaning to the sign bit in case of
707    /// a NaN, and as Rust doesn't guarantee that the bit pattern of NaNs are
708    /// conserved over arithmetic operations, the result of `is_sign_negative` on
709    /// a NaN might produce an unexpected or non-portable result. See the [specification
710    /// of NaN bit patterns](f32#nan-bit-patterns) for more info. Use `self.signum() == -1.0`
711    /// if you need fully portable behavior (will return `false` for all NaNs).
712    ///
713    /// ```
714    /// let f = 7.0_f64;
715    /// let g = -7.0_f64;
716    ///
717    /// assert!(!f.is_sign_negative());
718    /// assert!(g.is_sign_negative());
719    /// ```
720    #[must_use]
721    #[stable(feature = "rust1", since = "1.0.0")]
722    #[rustc_const_stable(feature = "const_float_classify", since = "1.83.0")]
723    #[inline]
724    pub const fn is_sign_negative(self) -> bool {
725        // IEEE754 says: isSignMinus(x) is true if and only if x has negative sign. isSignMinus
726        // applies to zeros and NaNs as well.
727        self.to_bits() & Self::SIGN_MASK != 0
728    }
729
730    #[must_use]
731    #[stable(feature = "rust1", since = "1.0.0")]
732    #[deprecated(since = "1.0.0", note = "renamed to is_sign_negative")]
733    #[inline]
734    #[doc(hidden)]
735    pub fn is_negative(self) -> bool {
736        self.is_sign_negative()
737    }
738
739    /// Returns the least number greater than `self`.
740    ///
741    /// Let `TINY` be the smallest representable positive `f64`. Then,
742    ///  - if `self.is_nan()`, this returns `self`;
743    ///  - if `self` is [`NEG_INFINITY`], this returns [`MIN`];
744    ///  - if `self` is `-TINY`, this returns -0.0;
745    ///  - if `self` is -0.0 or +0.0, this returns `TINY`;
746    ///  - if `self` is [`MAX`] or [`INFINITY`], this returns [`INFINITY`];
747    ///  - otherwise the unique least value greater than `self` is returned.
748    ///
749    /// The identity `x.next_up() == -(-x).next_down()` holds for all non-NaN `x`. When `x`
750    /// is finite `x == x.next_up().next_down()` also holds.
751    ///
752    /// ```rust
753    /// // f64::EPSILON is the difference between 1.0 and the next number up.
754    /// assert_eq!(1.0f64.next_up(), 1.0 + f64::EPSILON);
755    /// // But not for most numbers.
756    /// assert!(0.1f64.next_up() < 0.1 + f64::EPSILON);
757    /// assert_eq!(9007199254740992f64.next_up(), 9007199254740994.0);
758    /// ```
759    ///
760    /// This operation corresponds to IEEE-754 `nextUp`.
761    ///
762    /// [`NEG_INFINITY`]: Self::NEG_INFINITY
763    /// [`INFINITY`]: Self::INFINITY
764    /// [`MIN`]: Self::MIN
765    /// [`MAX`]: Self::MAX
766    #[inline]
767    #[doc(alias = "nextUp")]
768    #[stable(feature = "float_next_up_down", since = "1.86.0")]
769    #[rustc_const_stable(feature = "float_next_up_down", since = "1.86.0")]
770    pub const fn next_up(self) -> Self {
771        // Some targets violate Rust's assumption of IEEE semantics, e.g. by flushing
772        // denormals to zero. This is in general unsound and unsupported, but here
773        // we do our best to still produce the correct result on such targets.
774        let bits = self.to_bits();
775        if self.is_nan() || bits == Self::INFINITY.to_bits() {
776            return self;
777        }
778
779        let abs = bits & !Self::SIGN_MASK;
780        let next_bits = if abs == 0 {
781            Self::TINY_BITS
782        } else if bits == abs {
783            bits + 1
784        } else {
785            bits - 1
786        };
787        Self::from_bits(next_bits)
788    }
789
790    /// Returns the greatest number less than `self`.
791    ///
792    /// Let `TINY` be the smallest representable positive `f64`. Then,
793    ///  - if `self.is_nan()`, this returns `self`;
794    ///  - if `self` is [`INFINITY`], this returns [`MAX`];
795    ///  - if `self` is `TINY`, this returns 0.0;
796    ///  - if `self` is -0.0 or +0.0, this returns `-TINY`;
797    ///  - if `self` is [`MIN`] or [`NEG_INFINITY`], this returns [`NEG_INFINITY`];
798    ///  - otherwise the unique greatest value less than `self` is returned.
799    ///
800    /// The identity `x.next_down() == -(-x).next_up()` holds for all non-NaN `x`. When `x`
801    /// is finite `x == x.next_down().next_up()` also holds.
802    ///
803    /// ```rust
804    /// let x = 1.0f64;
805    /// // Clamp value into range [0, 1).
806    /// let clamped = x.clamp(0.0, 1.0f64.next_down());
807    /// assert!(clamped < 1.0);
808    /// assert_eq!(clamped.next_up(), 1.0);
809    /// ```
810    ///
811    /// This operation corresponds to IEEE-754 `nextDown`.
812    ///
813    /// [`NEG_INFINITY`]: Self::NEG_INFINITY
814    /// [`INFINITY`]: Self::INFINITY
815    /// [`MIN`]: Self::MIN
816    /// [`MAX`]: Self::MAX
817    #[inline]
818    #[doc(alias = "nextDown")]
819    #[stable(feature = "float_next_up_down", since = "1.86.0")]
820    #[rustc_const_stable(feature = "float_next_up_down", since = "1.86.0")]
821    pub const fn next_down(self) -> Self {
822        // Some targets violate Rust's assumption of IEEE semantics, e.g. by flushing
823        // denormals to zero. This is in general unsound and unsupported, but here
824        // we do our best to still produce the correct result on such targets.
825        let bits = self.to_bits();
826        if self.is_nan() || bits == Self::NEG_INFINITY.to_bits() {
827            return self;
828        }
829
830        let abs = bits & !Self::SIGN_MASK;
831        let next_bits = if abs == 0 {
832            Self::NEG_TINY_BITS
833        } else if bits == abs {
834            bits - 1
835        } else {
836            bits + 1
837        };
838        Self::from_bits(next_bits)
839    }
840
841    /// Takes the reciprocal (inverse) of a number, `1/x`.
842    ///
843    /// ```
844    /// let x = 2.0_f64;
845    /// let abs_difference = (x.recip() - (1.0 / x)).abs();
846    ///
847    /// assert!(abs_difference < 1e-10);
848    /// ```
849    #[must_use = "this returns the result of the operation, without modifying the original"]
850    #[stable(feature = "rust1", since = "1.0.0")]
851    #[rustc_const_stable(feature = "const_float_methods", since = "1.85.0")]
852    #[inline]
853    pub const fn recip(self) -> f64 {
854        1.0 / self
855    }
856
857    /// Converts radians to degrees.
858    ///
859    /// ```
860    /// let angle = std::f64::consts::PI;
861    ///
862    /// let abs_difference = (angle.to_degrees() - 180.0).abs();
863    ///
864    /// assert!(abs_difference < 1e-10);
865    /// ```
866    #[must_use = "this returns the result of the operation, \
867                  without modifying the original"]
868    #[stable(feature = "rust1", since = "1.0.0")]
869    #[rustc_const_stable(feature = "const_float_methods", since = "1.85.0")]
870    #[inline]
871    pub const fn to_degrees(self) -> f64 {
872        // The division here is correctly rounded with respect to the true
873        // value of 180/π. (This differs from f32, where a constant must be
874        // used to ensure a correctly rounded result.)
875        self * (180.0f64 / consts::PI)
876    }
877
878    /// Converts degrees to radians.
879    ///
880    /// ```
881    /// let angle = 180.0_f64;
882    ///
883    /// let abs_difference = (angle.to_radians() - std::f64::consts::PI).abs();
884    ///
885    /// assert!(abs_difference < 1e-10);
886    /// ```
887    #[must_use = "this returns the result of the operation, \
888                  without modifying the original"]
889    #[stable(feature = "rust1", since = "1.0.0")]
890    #[rustc_const_stable(feature = "const_float_methods", since = "1.85.0")]
891    #[inline]
892    pub const fn to_radians(self) -> f64 {
893        const RADS_PER_DEG: f64 = consts::PI / 180.0;
894        self * RADS_PER_DEG
895    }
896
897    /// Returns the maximum of the two numbers, ignoring NaN.
898    ///
899    /// If one of the arguments is NaN, then the other argument is returned.
900    /// This follows the IEEE 754-2008 semantics for maxNum, except for handling of signaling NaNs;
901    /// this function handles all NaNs the same way and avoids maxNum's problems with associativity.
902    /// This also matches the behavior of libm’s fmax. In particular, if the inputs compare equal
903    /// (such as for the case of `+0.0` and `-0.0`), either input may be returned non-deterministically.
904    ///
905    /// ```
906    /// let x = 1.0_f64;
907    /// let y = 2.0_f64;
908    ///
909    /// assert_eq!(x.max(y), y);
910    /// ```
911    #[must_use = "this returns the result of the comparison, without modifying either input"]
912    #[stable(feature = "rust1", since = "1.0.0")]
913    #[rustc_const_stable(feature = "const_float_methods", since = "1.85.0")]
914    #[inline]
915    pub const fn max(self, other: f64) -> f64 {
916        intrinsics::maxnumf64(self, other)
917    }
918
919    /// Returns the minimum of the two numbers, ignoring NaN.
920    ///
921    /// If one of the arguments is NaN, then the other argument is returned.
922    /// This follows the IEEE 754-2008 semantics for minNum, except for handling of signaling NaNs;
923    /// this function handles all NaNs the same way and avoids minNum's problems with associativity.
924    /// This also matches the behavior of libm’s fmin. In particular, if the inputs compare equal
925    /// (such as for the case of `+0.0` and `-0.0`), either input may be returned non-deterministically.
926    ///
927    /// ```
928    /// let x = 1.0_f64;
929    /// let y = 2.0_f64;
930    ///
931    /// assert_eq!(x.min(y), x);
932    /// ```
933    #[must_use = "this returns the result of the comparison, without modifying either input"]
934    #[stable(feature = "rust1", since = "1.0.0")]
935    #[rustc_const_stable(feature = "const_float_methods", since = "1.85.0")]
936    #[inline]
937    pub const fn min(self, other: f64) -> f64 {
938        intrinsics::minnumf64(self, other)
939    }
940
941    /// Returns the maximum of the two numbers, propagating NaN.
942    ///
943    /// This returns NaN when *either* argument is NaN, as opposed to
944    /// [`f64::max`] which only returns NaN when *both* arguments are NaN.
945    ///
946    /// ```
947    /// #![feature(float_minimum_maximum)]
948    /// let x = 1.0_f64;
949    /// let y = 2.0_f64;
950    ///
951    /// assert_eq!(x.maximum(y), y);
952    /// assert!(x.maximum(f64::NAN).is_nan());
953    /// ```
954    ///
955    /// If one of the arguments is NaN, then NaN is returned. Otherwise this returns the greater
956    /// of the two numbers. For this operation, -0.0 is considered to be less than +0.0.
957    /// Note that this follows the semantics specified in IEEE 754-2019.
958    ///
959    /// Also note that "propagation" of NaNs here doesn't necessarily mean that the bitpattern of a NaN
960    /// operand is conserved; see the [specification of NaN bit patterns](f32#nan-bit-patterns) for more info.
961    #[must_use = "this returns the result of the comparison, without modifying either input"]
962    #[unstable(feature = "float_minimum_maximum", issue = "91079")]
963    #[inline]
964    pub const fn maximum(self, other: f64) -> f64 {
965        intrinsics::maximumf64(self, other)
966    }
967
968    /// Returns the minimum of the two numbers, propagating NaN.
969    ///
970    /// This returns NaN when *either* argument is NaN, as opposed to
971    /// [`f64::min`] which only returns NaN when *both* arguments are NaN.
972    ///
973    /// ```
974    /// #![feature(float_minimum_maximum)]
975    /// let x = 1.0_f64;
976    /// let y = 2.0_f64;
977    ///
978    /// assert_eq!(x.minimum(y), x);
979    /// assert!(x.minimum(f64::NAN).is_nan());
980    /// ```
981    ///
982    /// If one of the arguments is NaN, then NaN is returned. Otherwise this returns the lesser
983    /// of the two numbers. For this operation, -0.0 is considered to be less than +0.0.
984    /// Note that this follows the semantics specified in IEEE 754-2019.
985    ///
986    /// Also note that "propagation" of NaNs here doesn't necessarily mean that the bitpattern of a NaN
987    /// operand is conserved; see the [specification of NaN bit patterns](f32#nan-bit-patterns) for more info.
988    #[must_use = "this returns the result of the comparison, without modifying either input"]
989    #[unstable(feature = "float_minimum_maximum", issue = "91079")]
990    #[inline]
991    pub const fn minimum(self, other: f64) -> f64 {
992        intrinsics::minimumf64(self, other)
993    }
994
995    /// Calculates the midpoint (average) between `self` and `rhs`.
996    ///
997    /// This returns NaN when *either* argument is NaN or if a combination of
998    /// +inf and -inf is provided as arguments.
999    ///
1000    /// # Examples
1001    ///
1002    /// ```
1003    /// assert_eq!(1f64.midpoint(4.0), 2.5);
1004    /// assert_eq!((-5.5f64).midpoint(8.0), 1.25);
1005    /// ```
1006    #[inline]
1007    #[doc(alias = "average")]
1008    #[stable(feature = "num_midpoint", since = "1.85.0")]
1009    #[rustc_const_stable(feature = "num_midpoint", since = "1.85.0")]
1010    pub const fn midpoint(self, other: f64) -> f64 {
1011        const LO: f64 = f64::MIN_POSITIVE * 2.;
1012        const HI: f64 = f64::MAX / 2.;
1013
1014        let (a, b) = (self, other);
1015        let abs_a = a.abs();
1016        let abs_b = b.abs();
1017
1018        if abs_a <= HI && abs_b <= HI {
1019            // Overflow is impossible
1020            (a + b) / 2.
1021        } else if abs_a < LO {
1022            // Not safe to halve `a` (would underflow)
1023            a + (b / 2.)
1024        } else if abs_b < LO {
1025            // Not safe to halve `b` (would underflow)
1026            (a / 2.) + b
1027        } else {
1028            // Safe to halve `a` and `b`
1029            (a / 2.) + (b / 2.)
1030        }
1031    }
1032
1033    /// Rounds toward zero and converts to any primitive integer type,
1034    /// assuming that the value is finite and fits in that type.
1035    ///
1036    /// ```
1037    /// let value = 4.6_f64;
1038    /// let rounded = unsafe { value.to_int_unchecked::<u16>() };
1039    /// assert_eq!(rounded, 4);
1040    ///
1041    /// let value = -128.9_f64;
1042    /// let rounded = unsafe { value.to_int_unchecked::<i8>() };
1043    /// assert_eq!(rounded, i8::MIN);
1044    /// ```
1045    ///
1046    /// # Safety
1047    ///
1048    /// The value must:
1049    ///
1050    /// * Not be `NaN`
1051    /// * Not be infinite
1052    /// * Be representable in the return type `Int`, after truncating off its fractional part
1053    #[must_use = "this returns the result of the operation, \
1054                  without modifying the original"]
1055    #[stable(feature = "float_approx_unchecked_to", since = "1.44.0")]
1056    #[inline]
1057    pub unsafe fn to_int_unchecked<Int>(self) -> Int
1058    where
1059        Self: FloatToInt<Int>,
1060    {
1061        // SAFETY: the caller must uphold the safety contract for
1062        // `FloatToInt::to_int_unchecked`.
1063        unsafe { FloatToInt::<Int>::to_int_unchecked(self) }
1064    }
1065
1066    /// Raw transmutation to `u64`.
1067    ///
1068    /// This is currently identical to `transmute::<f64, u64>(self)` on all platforms.
1069    ///
1070    /// See [`from_bits`](Self::from_bits) for some discussion of the
1071    /// portability of this operation (there are almost no issues).
1072    ///
1073    /// Note that this function is distinct from `as` casting, which attempts to
1074    /// preserve the *numeric* value, and not the bitwise value.
1075    ///
1076    /// # Examples
1077    ///
1078    /// ```
1079    /// assert!((1f64).to_bits() != 1f64 as u64); // to_bits() is not casting!
1080    /// assert_eq!((12.5f64).to_bits(), 0x4029000000000000);
1081    /// ```
1082    #[must_use = "this returns the result of the operation, \
1083                  without modifying the original"]
1084    #[stable(feature = "float_bits_conv", since = "1.20.0")]
1085    #[rustc_const_stable(feature = "const_float_bits_conv", since = "1.83.0")]
1086    #[allow(unnecessary_transmutes)]
1087    #[inline]
1088    pub const fn to_bits(self) -> u64 {
1089        // SAFETY: `u64` is a plain old datatype so we can always transmute to it.
1090        unsafe { mem::transmute(self) }
1091    }
1092
1093    /// Raw transmutation from `u64`.
1094    ///
1095    /// This is currently identical to `transmute::<u64, f64>(v)` on all platforms.
1096    /// It turns out this is incredibly portable, for two reasons:
1097    ///
1098    /// * Floats and Ints have the same endianness on all supported platforms.
1099    /// * IEEE 754 very precisely specifies the bit layout of floats.
1100    ///
1101    /// However there is one caveat: prior to the 2008 version of IEEE 754, how
1102    /// to interpret the NaN signaling bit wasn't actually specified. Most platforms
1103    /// (notably x86 and ARM) picked the interpretation that was ultimately
1104    /// standardized in 2008, but some didn't (notably MIPS). As a result, all
1105    /// signaling NaNs on MIPS are quiet NaNs on x86, and vice-versa.
1106    ///
1107    /// Rather than trying to preserve signaling-ness cross-platform, this
1108    /// implementation favors preserving the exact bits. This means that
1109    /// any payloads encoded in NaNs will be preserved even if the result of
1110    /// this method is sent over the network from an x86 machine to a MIPS one.
1111    ///
1112    /// If the results of this method are only manipulated by the same
1113    /// architecture that produced them, then there is no portability concern.
1114    ///
1115    /// If the input isn't NaN, then there is no portability concern.
1116    ///
1117    /// If you don't care about signaling-ness (very likely), then there is no
1118    /// portability concern.
1119    ///
1120    /// Note that this function is distinct from `as` casting, which attempts to
1121    /// preserve the *numeric* value, and not the bitwise value.
1122    ///
1123    /// # Examples
1124    ///
1125    /// ```
1126    /// let v = f64::from_bits(0x4029000000000000);
1127    /// assert_eq!(v, 12.5);
1128    /// ```
1129    #[stable(feature = "float_bits_conv", since = "1.20.0")]
1130    #[rustc_const_stable(feature = "const_float_bits_conv", since = "1.83.0")]
1131    #[must_use]
1132    #[inline]
1133    #[allow(unnecessary_transmutes)]
1134    pub const fn from_bits(v: u64) -> Self {
1135        // It turns out the safety issues with sNaN were overblown! Hooray!
1136        // SAFETY: `u64` is a plain old datatype so we can always transmute from it.
1137        unsafe { mem::transmute(v) }
1138    }
1139
1140    /// Returns the memory representation of this floating point number as a byte array in
1141    /// big-endian (network) byte order.
1142    ///
1143    /// See [`from_bits`](Self::from_bits) for some discussion of the
1144    /// portability of this operation (there are almost no issues).
1145    ///
1146    /// # Examples
1147    ///
1148    /// ```
1149    /// let bytes = 12.5f64.to_be_bytes();
1150    /// assert_eq!(bytes, [0x40, 0x29, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00]);
1151    /// ```
1152    #[must_use = "this returns the result of the operation, \
1153                  without modifying the original"]
1154    #[stable(feature = "float_to_from_bytes", since = "1.40.0")]
1155    #[rustc_const_stable(feature = "const_float_bits_conv", since = "1.83.0")]
1156    #[inline]
1157    pub const fn to_be_bytes(self) -> [u8; 8] {
1158        self.to_bits().to_be_bytes()
1159    }
1160
1161    /// Returns the memory representation of this floating point number as a byte array in
1162    /// little-endian byte order.
1163    ///
1164    /// See [`from_bits`](Self::from_bits) for some discussion of the
1165    /// portability of this operation (there are almost no issues).
1166    ///
1167    /// # Examples
1168    ///
1169    /// ```
1170    /// let bytes = 12.5f64.to_le_bytes();
1171    /// assert_eq!(bytes, [0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x29, 0x40]);
1172    /// ```
1173    #[must_use = "this returns the result of the operation, \
1174                  without modifying the original"]
1175    #[stable(feature = "float_to_from_bytes", since = "1.40.0")]
1176    #[rustc_const_stable(feature = "const_float_bits_conv", since = "1.83.0")]
1177    #[inline]
1178    pub const fn to_le_bytes(self) -> [u8; 8] {
1179        self.to_bits().to_le_bytes()
1180    }
1181
1182    /// Returns the memory representation of this floating point number as a byte array in
1183    /// native byte order.
1184    ///
1185    /// As the target platform's native endianness is used, portable code
1186    /// should use [`to_be_bytes`] or [`to_le_bytes`], as appropriate, instead.
1187    ///
1188    /// [`to_be_bytes`]: f64::to_be_bytes
1189    /// [`to_le_bytes`]: f64::to_le_bytes
1190    ///
1191    /// See [`from_bits`](Self::from_bits) for some discussion of the
1192    /// portability of this operation (there are almost no issues).
1193    ///
1194    /// # Examples
1195    ///
1196    /// ```
1197    /// let bytes = 12.5f64.to_ne_bytes();
1198    /// assert_eq!(
1199    ///     bytes,
1200    ///     if cfg!(target_endian = "big") {
1201    ///         [0x40, 0x29, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00]
1202    ///     } else {
1203    ///         [0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x29, 0x40]
1204    ///     }
1205    /// );
1206    /// ```
1207    #[must_use = "this returns the result of the operation, \
1208                  without modifying the original"]
1209    #[stable(feature = "float_to_from_bytes", since = "1.40.0")]
1210    #[rustc_const_stable(feature = "const_float_bits_conv", since = "1.83.0")]
1211    #[inline]
1212    pub const fn to_ne_bytes(self) -> [u8; 8] {
1213        self.to_bits().to_ne_bytes()
1214    }
1215
1216    /// Creates a floating point value from its representation as a byte array in big endian.
1217    ///
1218    /// See [`from_bits`](Self::from_bits) for some discussion of the
1219    /// portability of this operation (there are almost no issues).
1220    ///
1221    /// # Examples
1222    ///
1223    /// ```
1224    /// let value = f64::from_be_bytes([0x40, 0x29, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00]);
1225    /// assert_eq!(value, 12.5);
1226    /// ```
1227    #[stable(feature = "float_to_from_bytes", since = "1.40.0")]
1228    #[rustc_const_stable(feature = "const_float_bits_conv", since = "1.83.0")]
1229    #[must_use]
1230    #[inline]
1231    pub const fn from_be_bytes(bytes: [u8; 8]) -> Self {
1232        Self::from_bits(u64::from_be_bytes(bytes))
1233    }
1234
1235    /// Creates a floating point value from its representation as a byte array in little endian.
1236    ///
1237    /// See [`from_bits`](Self::from_bits) for some discussion of the
1238    /// portability of this operation (there are almost no issues).
1239    ///
1240    /// # Examples
1241    ///
1242    /// ```
1243    /// let value = f64::from_le_bytes([0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x29, 0x40]);
1244    /// assert_eq!(value, 12.5);
1245    /// ```
1246    #[stable(feature = "float_to_from_bytes", since = "1.40.0")]
1247    #[rustc_const_stable(feature = "const_float_bits_conv", since = "1.83.0")]
1248    #[must_use]
1249    #[inline]
1250    pub const fn from_le_bytes(bytes: [u8; 8]) -> Self {
1251        Self::from_bits(u64::from_le_bytes(bytes))
1252    }
1253
1254    /// Creates a floating point value from its representation as a byte array in native endian.
1255    ///
1256    /// As the target platform's native endianness is used, portable code
1257    /// likely wants to use [`from_be_bytes`] or [`from_le_bytes`], as
1258    /// appropriate instead.
1259    ///
1260    /// [`from_be_bytes`]: f64::from_be_bytes
1261    /// [`from_le_bytes`]: f64::from_le_bytes
1262    ///
1263    /// See [`from_bits`](Self::from_bits) for some discussion of the
1264    /// portability of this operation (there are almost no issues).
1265    ///
1266    /// # Examples
1267    ///
1268    /// ```
1269    /// let value = f64::from_ne_bytes(if cfg!(target_endian = "big") {
1270    ///     [0x40, 0x29, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00]
1271    /// } else {
1272    ///     [0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x29, 0x40]
1273    /// });
1274    /// assert_eq!(value, 12.5);
1275    /// ```
1276    #[stable(feature = "float_to_from_bytes", since = "1.40.0")]
1277    #[rustc_const_stable(feature = "const_float_bits_conv", since = "1.83.0")]
1278    #[must_use]
1279    #[inline]
1280    pub const fn from_ne_bytes(bytes: [u8; 8]) -> Self {
1281        Self::from_bits(u64::from_ne_bytes(bytes))
1282    }
1283
1284    /// Returns the ordering between `self` and `other`.
1285    ///
1286    /// Unlike the standard partial comparison between floating point numbers,
1287    /// this comparison always produces an ordering in accordance to
1288    /// the `totalOrder` predicate as defined in the IEEE 754 (2008 revision)
1289    /// floating point standard. The values are ordered in the following sequence:
1290    ///
1291    /// - negative quiet NaN
1292    /// - negative signaling NaN
1293    /// - negative infinity
1294    /// - negative numbers
1295    /// - negative subnormal numbers
1296    /// - negative zero
1297    /// - positive zero
1298    /// - positive subnormal numbers
1299    /// - positive numbers
1300    /// - positive infinity
1301    /// - positive signaling NaN
1302    /// - positive quiet NaN.
1303    ///
1304    /// The ordering established by this function does not always agree with the
1305    /// [`PartialOrd`] and [`PartialEq`] implementations of `f64`. For example,
1306    /// they consider negative and positive zero equal, while `total_cmp`
1307    /// doesn't.
1308    ///
1309    /// The interpretation of the signaling NaN bit follows the definition in
1310    /// the IEEE 754 standard, which may not match the interpretation by some of
1311    /// the older, non-conformant (e.g. MIPS) hardware implementations.
1312    ///
1313    /// # Example
1314    ///
1315    /// ```
1316    /// struct GoodBoy {
1317    ///     name: String,
1318    ///     weight: f64,
1319    /// }
1320    ///
1321    /// let mut bois = vec![
1322    ///     GoodBoy { name: "Pucci".to_owned(), weight: 0.1 },
1323    ///     GoodBoy { name: "Woofer".to_owned(), weight: 99.0 },
1324    ///     GoodBoy { name: "Yapper".to_owned(), weight: 10.0 },
1325    ///     GoodBoy { name: "Chonk".to_owned(), weight: f64::INFINITY },
1326    ///     GoodBoy { name: "Abs. Unit".to_owned(), weight: f64::NAN },
1327    ///     GoodBoy { name: "Floaty".to_owned(), weight: -5.0 },
1328    /// ];
1329    ///
1330    /// bois.sort_by(|a, b| a.weight.total_cmp(&b.weight));
1331    ///
1332    /// // `f64::NAN` could be positive or negative, which will affect the sort order.
1333    /// if f64::NAN.is_sign_negative() {
1334    ///     assert!(bois.into_iter().map(|b| b.weight)
1335    ///         .zip([f64::NAN, -5.0, 0.1, 10.0, 99.0, f64::INFINITY].iter())
1336    ///         .all(|(a, b)| a.to_bits() == b.to_bits()))
1337    /// } else {
1338    ///     assert!(bois.into_iter().map(|b| b.weight)
1339    ///         .zip([-5.0, 0.1, 10.0, 99.0, f64::INFINITY, f64::NAN].iter())
1340    ///         .all(|(a, b)| a.to_bits() == b.to_bits()))
1341    /// }
1342    /// ```
1343    #[stable(feature = "total_cmp", since = "1.62.0")]
1344    #[must_use]
1345    #[inline]
1346    pub fn total_cmp(&self, other: &Self) -> crate::cmp::Ordering {
1347        let mut left = self.to_bits() as i64;
1348        let mut right = other.to_bits() as i64;
1349
1350        // In case of negatives, flip all the bits except the sign
1351        // to achieve a similar layout as two's complement integers
1352        //
1353        // Why does this work? IEEE 754 floats consist of three fields:
1354        // Sign bit, exponent and mantissa. The set of exponent and mantissa
1355        // fields as a whole have the property that their bitwise order is
1356        // equal to the numeric magnitude where the magnitude is defined.
1357        // The magnitude is not normally defined on NaN values, but
1358        // IEEE 754 totalOrder defines the NaN values also to follow the
1359        // bitwise order. This leads to order explained in the doc comment.
1360        // However, the representation of magnitude is the same for negative
1361        // and positive numbers – only the sign bit is different.
1362        // To easily compare the floats as signed integers, we need to
1363        // flip the exponent and mantissa bits in case of negative numbers.
1364        // We effectively convert the numbers to "two's complement" form.
1365        //
1366        // To do the flipping, we construct a mask and XOR against it.
1367        // We branchlessly calculate an "all-ones except for the sign bit"
1368        // mask from negative-signed values: right shifting sign-extends
1369        // the integer, so we "fill" the mask with sign bits, and then
1370        // convert to unsigned to push one more zero bit.
1371        // On positive values, the mask is all zeros, so it's a no-op.
1372        left ^= (((left >> 63) as u64) >> 1) as i64;
1373        right ^= (((right >> 63) as u64) >> 1) as i64;
1374
1375        left.cmp(&right)
1376    }
1377
1378    /// Restrict a value to a certain interval unless it is NaN.
1379    ///
1380    /// Returns `max` if `self` is greater than `max`, and `min` if `self` is
1381    /// less than `min`. Otherwise this returns `self`.
1382    ///
1383    /// Note that this function returns NaN if the initial value was NaN as
1384    /// well.
1385    ///
1386    /// # Panics
1387    ///
1388    /// Panics if `min > max`, `min` is NaN, or `max` is NaN.
1389    ///
1390    /// # Examples
1391    ///
1392    /// ```
1393    /// assert!((-3.0f64).clamp(-2.0, 1.0) == -2.0);
1394    /// assert!((0.0f64).clamp(-2.0, 1.0) == 0.0);
1395    /// assert!((2.0f64).clamp(-2.0, 1.0) == 1.0);
1396    /// assert!((f64::NAN).clamp(-2.0, 1.0).is_nan());
1397    /// ```
1398    #[must_use = "method returns a new number and does not mutate the original value"]
1399    #[stable(feature = "clamp", since = "1.50.0")]
1400    #[rustc_const_stable(feature = "const_float_methods", since = "1.85.0")]
1401    #[inline]
1402    pub const fn clamp(mut self, min: f64, max: f64) -> f64 {
1403        const_assert!(
1404            min <= max,
1405            "min > max, or either was NaN",
1406            "min > max, or either was NaN. min = {min:?}, max = {max:?}",
1407            min: f64,
1408            max: f64,
1409        );
1410
1411        if self < min {
1412            self = min;
1413        }
1414        if self > max {
1415            self = max;
1416        }
1417        self
1418    }
1419
1420    /// Computes the absolute value of `self`.
1421    ///
1422    /// This function always returns the precise result.
1423    ///
1424    /// # Examples
1425    ///
1426    /// ```
1427    /// let x = 3.5_f64;
1428    /// let y = -3.5_f64;
1429    ///
1430    /// assert_eq!(x.abs(), x);
1431    /// assert_eq!(y.abs(), -y);
1432    ///
1433    /// assert!(f64::NAN.abs().is_nan());
1434    /// ```
1435    #[must_use = "method returns a new number and does not mutate the original value"]
1436    #[stable(feature = "rust1", since = "1.0.0")]
1437    #[rustc_const_stable(feature = "const_float_methods", since = "1.85.0")]
1438    #[inline]
1439    pub const fn abs(self) -> f64 {
1440        // SAFETY: this is actually a safe intrinsic
1441        unsafe { intrinsics::fabsf64(self) }
1442    }
1443
1444    /// Returns a number that represents the sign of `self`.
1445    ///
1446    /// - `1.0` if the number is positive, `+0.0` or `INFINITY`
1447    /// - `-1.0` if the number is negative, `-0.0` or `NEG_INFINITY`
1448    /// - NaN if the number is NaN
1449    ///
1450    /// # Examples
1451    ///
1452    /// ```
1453    /// let f = 3.5_f64;
1454    ///
1455    /// assert_eq!(f.signum(), 1.0);
1456    /// assert_eq!(f64::NEG_INFINITY.signum(), -1.0);
1457    ///
1458    /// assert!(f64::NAN.signum().is_nan());
1459    /// ```
1460    #[must_use = "method returns a new number and does not mutate the original value"]
1461    #[stable(feature = "rust1", since = "1.0.0")]
1462    #[rustc_const_stable(feature = "const_float_methods", since = "1.85.0")]
1463    #[inline]
1464    pub const fn signum(self) -> f64 {
1465        if self.is_nan() { Self::NAN } else { 1.0_f64.copysign(self) }
1466    }
1467
1468    /// Returns a number composed of the magnitude of `self` and the sign of
1469    /// `sign`.
1470    ///
1471    /// Equal to `self` if the sign of `self` and `sign` are the same, otherwise equal to `-self`.
1472    /// If `self` is a NaN, then a NaN with the same payload as `self` and the sign bit of `sign` is
1473    /// returned.
1474    ///
1475    /// If `sign` is a NaN, then this operation will still carry over its sign into the result. Note
1476    /// that IEEE 754 doesn't assign any meaning to the sign bit in case of a NaN, and as Rust
1477    /// doesn't guarantee that the bit pattern of NaNs are conserved over arithmetic operations, the
1478    /// result of `copysign` with `sign` being a NaN might produce an unexpected or non-portable
1479    /// result. See the [specification of NaN bit patterns](primitive@f32#nan-bit-patterns) for more
1480    /// info.
1481    ///
1482    /// # Examples
1483    ///
1484    /// ```
1485    /// let f = 3.5_f64;
1486    ///
1487    /// assert_eq!(f.copysign(0.42), 3.5_f64);
1488    /// assert_eq!(f.copysign(-0.42), -3.5_f64);
1489    /// assert_eq!((-f).copysign(0.42), 3.5_f64);
1490    /// assert_eq!((-f).copysign(-0.42), -3.5_f64);
1491    ///
1492    /// assert!(f64::NAN.copysign(1.0).is_nan());
1493    /// ```
1494    #[must_use = "method returns a new number and does not mutate the original value"]
1495    #[stable(feature = "copysign", since = "1.35.0")]
1496    #[rustc_const_stable(feature = "const_float_methods", since = "1.85.0")]
1497    #[inline]
1498    pub const fn copysign(self, sign: f64) -> f64 {
1499        // SAFETY: this is actually a safe intrinsic
1500        unsafe { intrinsics::copysignf64(self, sign) }
1501    }
1502
1503    /// Float addition that allows optimizations based on algebraic rules.
1504    ///
1505    /// See [algebraic operators](primitive@f32#algebraic-operators) for more info.
1506    #[must_use = "method returns a new number and does not mutate the original value"]
1507    #[unstable(feature = "float_algebraic", issue = "136469")]
1508    #[rustc_const_unstable(feature = "float_algebraic", issue = "136469")]
1509    #[inline]
1510    pub const fn algebraic_add(self, rhs: f64) -> f64 {
1511        intrinsics::fadd_algebraic(self, rhs)
1512    }
1513
1514    /// Float subtraction that allows optimizations based on algebraic rules.
1515    ///
1516    /// See [algebraic operators](primitive@f32#algebraic-operators) for more info.
1517    #[must_use = "method returns a new number and does not mutate the original value"]
1518    #[unstable(feature = "float_algebraic", issue = "136469")]
1519    #[rustc_const_unstable(feature = "float_algebraic", issue = "136469")]
1520    #[inline]
1521    pub const fn algebraic_sub(self, rhs: f64) -> f64 {
1522        intrinsics::fsub_algebraic(self, rhs)
1523    }
1524
1525    /// Float multiplication that allows optimizations based on algebraic rules.
1526    ///
1527    /// See [algebraic operators](primitive@f32#algebraic-operators) for more info.
1528    #[must_use = "method returns a new number and does not mutate the original value"]
1529    #[unstable(feature = "float_algebraic", issue = "136469")]
1530    #[rustc_const_unstable(feature = "float_algebraic", issue = "136469")]
1531    #[inline]
1532    pub const fn algebraic_mul(self, rhs: f64) -> f64 {
1533        intrinsics::fmul_algebraic(self, rhs)
1534    }
1535
1536    /// Float division that allows optimizations based on algebraic rules.
1537    ///
1538    /// See [algebraic operators](primitive@f32#algebraic-operators) for more info.
1539    #[must_use = "method returns a new number and does not mutate the original value"]
1540    #[unstable(feature = "float_algebraic", issue = "136469")]
1541    #[rustc_const_unstable(feature = "float_algebraic", issue = "136469")]
1542    #[inline]
1543    pub const fn algebraic_div(self, rhs: f64) -> f64 {
1544        intrinsics::fdiv_algebraic(self, rhs)
1545    }
1546
1547    /// Float remainder that allows optimizations based on algebraic rules.
1548    ///
1549    /// See [algebraic operators](primitive@f32#algebraic-operators) for more info.
1550    #[must_use = "method returns a new number and does not mutate the original value"]
1551    #[unstable(feature = "float_algebraic", issue = "136469")]
1552    #[rustc_const_unstable(feature = "float_algebraic", issue = "136469")]
1553    #[inline]
1554    pub const fn algebraic_rem(self, rhs: f64) -> f64 {
1555        intrinsics::frem_algebraic(self, rhs)
1556    }
1557}